Satellites of an oriented surface link and their local moves
Satellites of an oriented surface link and their local moves
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定向表面链路的卫星及其本地移动
DOI：
10.1016/j.topol.2013.12.010
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Inasa NAKAMURA
中科院分区：
文献类型：
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作者：
Shunsuke Tomita;Tomohiro Soejima;Keitaro Yoshimoto;Shunsuke Tomita;冨田峻介;冨田峻介;Shunsuke Tbmita;Kenta Kimura;Kenta Kimura;木村健太;木村健太;木村健太;Kenta Kimura;Inasa NAKAMURA
对于R4中的有向曲面链F，我们考虑F上的一个曲面链的卫星构造，称为F上的二维辫子，它的形式是F上的覆盖.我们在F的曲面图π(F)⊂R3上引入了m-图的概念，它是π(F)上满足一定条件的有限图，是2-圆盘上表示曲面辫子的m-图的推广.用π(F)上的m图表示了F上的二维辫子。已知两个表面链是等价的，当且仅当它们的表面图由R3的环境同位素和称为罗斯曼运动的局部运动的有限序列联系在一起。我们证明了具有m图的曲面图的Roseman运动是可以很好地定义的。
For an oriented surface link F in R 4, we consider a satellite construction of a surface link, called a 2-dimensional braid over F, which is in the form of a covering over F. We introduce the notion of an m-chart on a surface diagram π (F)⊂ R 3 of F, which is a finite graph on π (F) satisfying certain conditions and is an extended notion of an m-chart on a 2-disk presenting a surface braid. A 2-dimensional braid over F is presented by an m-chart on π (F). It is known that two surface links are equivalent if and only if their surface diagrams are related by a finite sequence of ambient isotopies of R 3 and local moves called Roseman moves. We show that Roseman moves for surface diagrams with m-charts can be well-defined.